Rugby Science

January 28 2013

Studying the Gyroscopic Effect of a Prolate Spheroid in Motion aka The Spin Pass

posted Jan 28 2013
[ed. comments below]

As rugby people know, the world is not round, it's ellipsoid. In actuality the earth is wider at the equator than at the poles giving it a shape of an oblate spheroid, defined as "a rotationally symmetric ellipsoid having a polar axis shorter than the diameter of the equatorial circle whose plane bisects it". A rugby ball on the other hand is a prolate spheroid which is "a spheroid in which the polar axis is greater than the equatorial diameter".

So with that out of the way let's take a look at this prolate spheroid we call a rugby ball. Here are some facts:

The specifications of all size 5 rugby balls are determined by the International Rugby Board (iRB)

The ball must be oval and made of four panels.
Length in line 280 - 300 millimeters
Circumference (end to end) 740 - 770 millimeters
Circumference (in width) 580 - 620 millimeters
Material: Leather or suitable synthetic material. It may be treated to make it water resistant and easier to grip.
Weight: 410 - 460 grams
Air pressure at start of play: 65.71-68.75 kilopascals, or 0.67-0.70 kilograms per square centimeter, or 9.5-10.0 lbs per square inch.

Why spin a rugby ball? In order to make it go further with more accuracy and the two scientific principles involved are aerodynamics and gyroscopic effect.

The illustration below visually demonstrates the variation of air flow at different yaw angles of a rugby ball in flight. It can be seen that at 0 degrees there is less air turbulence and hence less air friction to slow the ball down. So how do you keep a ball stable enough to maintain that angle during flight, that's where gyroscopic effect comes into play due to the principles of angular momentum aka the spin.

So if someone asks what you do at the rugby club you can tell them you are studying the gyroscopic effect of a prolate spheroid in motion but we'll know you are practicing your spin pass.

Aerodynamics of a rugby ball

Pemberton Holmes
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